Asymptotic Bound on Binary Self-Orthogonal Codes

TL;DR

This paper introduces two new constructions for binary self-orthogonal codes, providing a constructive lower bound on their parameters and proving they asymptotically reach the Gilbert-Varshamov bound.

Contribution

The paper presents novel constructions for binary self-orthogonal codes and establishes their asymptotic optimality relative to the Gilbert-Varshamov bound.

Findings

Constructive lower bound on minimum distance for rate 1/2 codes

Codes asymptotically achieve Gilbert-Varshamov bound

Relative minimum distance approximately 0.0595 at rate 1/2

Abstract

We present two constructions for binary self-orthogonal codes. It turns out that our constructions yield a constructive bound on binary self-orthogonal codes. In particular, when the information rate R=1/2, by our constructive lower bound, the relative minimum distance \delta\approx 0.0595 (for GV bound, \delta\approx 0.110). Moreover, we have proved that the binary self-orthogonal codes asymptotically achieve the Gilbert-Varshamov bound.